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The geometry of one-loop amplitudes

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arxiv 1010.5334 v1 pith:FG6AXUTV submitted 2010-10-26 hep-th

Oliver Schnetz This is my paper · ORCID
classification hep-th
keywords calculationgeometryamplitudecaseformulaone-loopreductionamplitudes
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We review a reduction formula by Petersson that reduces the calculation of a one-loop amplitude with N external lines in n<N space-time dimensions to the case n=N and give it a geometric interpretation. In the case n=N the calculation of the euclidean amplitude is shown to be equivalent to the calculation of the volume of a tetrahedron spanned by the momenta in (n-1)-dimensional hyperbolic space. The underlying geometry is intimately linked to the geometry of the reduction formula.

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  1. Recursive construction of scalar one-loop integrals in dimensional regularisation

    hep-th 2026-07 conditional novelty 8.0 of 10

    A recursion based on hyperbolic simplex volumes expresses every epsilon-expansion coefficient of scalar one-loop Feynman integrals in terms of multiple polylogarithms.

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